Vortex quantum dynamics of two dimensional lattice bosons

TL;DR

This paper investigates the quantum melting of vortex lattices into a vortex liquid in two-dimensional bosonic systems, revealing a critical density for melting, vortex spin properties, and Hall conductivity behavior.

Contribution

It provides a detailed analysis of vortex quantum dynamics, including the vortex hopping rate, Hall conductivity, and vortex spin at half filling, offering new insights into vortex lattice melting mechanisms.

Findings

Quantum vortex lattice melts into a vortex liquid above a critical density of 0.0065 vortices per site.

Hall conductivity reverses sign at half filling, indicating a sharp transition.

Vortices carry a spin-half quantum number (`v-spin') at half filling due to SU(2) symmetries.

Abstract

In two dimensions a vortex lattice can melt by quantum fluctuations into a non-superfluid Quantum Vortex Liquid (QVL). To determine the melting conditions, we compute the bare vortex hopping rate by exact diagonalization of square clusters near half filling. Mapping our effective Hamiltonian to the Boson Coloumb Liquid simulated in Phys. Rev. Lett. 73, 826 (1994), we expect a QVL above a melting density of 0.0065 vortices per lattice site. We also compute the Hall conductivity using adiabatic curvatures. As a function of boson filling it reverses sign at half filling in a sharp transition accompanied by a vanishing temperature scale. At half filling, each vortex carries a spin half quantum number (`v-spin'), as a consequence of local non commuting SU(2) symmetries. Implications of these results could be realized in cold atoms, Josephson junction arrays and cuprate superconductors.